Not applicable
The field of the invention is AC induction motor drives and more specifically the area of injecting high frequency voltage signals into an AC induction motor and using high frequency feedback signals to identify stator flux position.
Induction motors have broad application in industry, particularly when large horsepower is needed. In a three-phase induction motor, three phase alternating voltages are impressed across three separate motor stator windings and cause three phase currents therein. Because of inductances, the three currents typically lag the voltages by some phase angle. The three currents produce a rotating magnetic stator field. A rotor contained within the stator field experiences an induced current (hence the term xe2x80x9cinductionxe2x80x9d) which generates a rotor field. The rotor field typically lags the stator field by some phase angle. The rotor field is attracted to the rotating stator field and the interaction between the two fields causes the rotor to rotate.
A common rotor design includes a xe2x80x9csquirrel cage windingxe2x80x9d in which axial conductive bars are connected at either end by shorting rings to form a generally cylindrical structure. The flux of the stator field cutting across the conductive bars induces cyclic current flows through the bars and across the shorting rings. The cyclic current flows in turn produce the rotor field. The use of this induced current to generate the rotor field eliminates the need for slip rings or brushes to provide power to the rotor, making the design relatively maintenance free.
To a first approximation, the torque and speed of an induction motor may be controlled by changing the frequency of the driving voltage and thus the angular rate of the rotating stator field. Generally, for a given torque, increasing the stator field rate will increase the speed of the rotor (which follows the stator field). Alternatively, for a given rotor speed, increasing the frequency of the stator field will increase the torque by increasing the slip, that is the difference in speed between the rotor and the stator fields. An increase in slip increases the rate at which flux lines are cut by the rotor, increasing the rotor generated field and thus the force or torque between the rotor and stator fields.
Referring to FIG. 1, a rotating phasor 1 corresponding to a stator magneto motive force (xe2x80x9cmmfxe2x80x9d) will generally have some angle xcex1 with respect to the phasor of rotor flux 2. The torque generated by the motor will be proportional to the magnitudes of these phasors 1 and 2 but also will be a function of their angle xcex1. Maximum torque is produced when phasors 1 and 2 are at right angles to each other whereas zero torque is produced if the phasors are aligned. The stator mmf phasor 1 may therefore be usefully decomposed into a torque producing component 3 perpendicular to rotor flux phasor 2 and a flux component 4 parallel to rotor flux phasor 2.
These two components 3 and 4 of the stator mmf are proportional, respectively, to two stator current components: iq, a torque producing current, and id, a flux producing current, which may be represented by quadrature or orthogonal vectors in a rotating or synchronous frame of reference (i.e., a reference frame that rotates along with the stator flux vector) and each vector iq and id is characterized by slowly varying DC magnitude.
Accordingly, in controlling an induction motor, it is generally desired to control not only the frequency of the applied voltage (hence the speed of the rotation of the stator flux phasor 1), but also the phase of the applied voltage relative to the current flow and hence the division of the currents through the stator windings into the iq and id components. Control strategies that attempt to independently control current components iq and id are generally referred to as field oriented control strategies (xe2x80x9cFOCxe2x80x9d).
Generally, it is desirable to design FOC strategies that are capable of driving motors of many different designs and varying sizes. Such versatility cuts down on research, development, and manufacturing costs and also results in easily serviceable controllers. Unfortunately, while versatile controllers are cost-effective, FOC controllers cannot control motor operation precisely unless they can adjust the division of d and q-axis currents through the stator windings to account for motor-specific operating parameters. For this reason, in order to increase motor operating precision, various feedback loops are typically employed to monitor stator winding currents and voltages and/or motor speed. A controller uses feedback information to determine how the inverter supplied voltage must be altered to compensate for system disturbances due to system specific and often dynamic operating parameters and then adjusts control signals to supply the desired inverter voltages.
To this end, in an exemplary FOC system, two phase d and q-axis command currents are provided that are calculated to control a motor in a desired fashion. The command currents are compared to d and q-axis motor feedback currents to generate error signals (i.e., the differences between the command and feedback currents). The error signals are then used to generate d and q-axis command voltage signals which are in turn transformed into three phase command voltage signals, one voltage signal for each of the three motor phases. The command voltage signals are used to drive a pulse width modulated (PWM) inverter that generates voltages on three motor supply lines. To provide the d and q-axis current feedback signals the system typically includes current sensors to sense the three phase line currents and a coordinate transformation block is used to transform the three phase currents to two phase synchronous dq frame of reference feedback currents.
In addition to requiring two phase signals and three phase signals to perform 2-to-3 and 3-to-2 phase transformations, respectively, a precise flux position angle estimate xcex8xe2x80x2m is also required. One common way to generate a flux angle feedback estimate is to integrate a stator frequency. A stator frequency can be determined by adding a measured rotor frequency (rotor speed) and a calculated slip frequency. In the case of drives that do not include a rotor speed sensor, it is necessary to estimate both the rotor frequency and the slip frequency to determine the flux angle. Thus, these drives require precise knowledge of motor parameter values.
In an effort to reduce system costs and increase reliability, the controls industry has recently developed various types of sensorless or self-sensing induction machine systems that, as the labels imply, do not include dedicated speed sensing hardware and corresponding cabling but that, nevertheless, can generate accurate position, flux and velocity estimates. Techniques used for operating parameter estimation can be divided into two groups including techniques that track speed dependent phenomenon and techniques that track spatial saliencies in system signals. These techniques generally use disturbances in d and q-axis feedback currents to identify the operating parameters of interest and hence provide additional functionality which, in effect, xe2x80x9cpiggy-backsxe2x80x9d on feedback signals that are obtained for another purpose (i.e., dq current components are already required for FOC).
Because speed dependent techniques depend on speed in order to generate an identifiable feedback signal, these techniques ultimately fail at zero or low (e.g., below 5 Hz) excitation frequency due to lack of signal. In addition, because these methods estimate operating parameters from voltage and current, these techniques are sensitive to temperature varying system parameters such as stator resistance, etc.
One type of saliency tracking technique includes injecting or applying a known high frequency xe2x80x9cinjectionxe2x80x9d voltage signal in addition to each of the command voltage signals used to drive the PWM inverter and using feedback current (or voltage) signals to identify saliencies associated with the flux angle. To this end, an exemplary system converts a high frequency command signal into a high frequency phase angle and generates a first injection signal that is the product of a scalar and the sine of the high frequency phase angle. Second and third injection signals are also generated, each of the second and third signals phase shifted from the first signal by 120 degrees. A separate one of the first, second and third signals is then added to a separate one of the three voltage command signals that are used to drive the PWM inverter.
One injection type saliency tracking algorithm to generate a flux position angle estimate without a rotor speed sensor employs a negative sequence of the high frequency current component and is described in an article that issued in the IEEE Transactions on Industry Applications publication, vol. 34, No. 5, September/October 1998 by Robert Lorenz which is entitled xe2x80x9cUsing Multiple Saliencies For The Estimation Of Flux Position, And Velocity In AC Machinesxe2x80x9d (hereinafter xe2x80x9cthe Lorenz articlexe2x80x9d). The algorithm in the Lorenz article is based on the fact that when a high frequency voltage signal (referred to in the Lorenz article as a xe2x80x9ccarrier signalxe2x80x9d) is injected into a rotating system, a resulting high frequency field interacts with system saliency to produce a xe2x80x9ccarrierxe2x80x9d signal current that contains information relating to the position of the saliency. The carrier current consists of both positive and negative-sequence components relative to the carrier signal voltage excitation. While the positive sequence component rotates in the same direction as the carrier signal voltage excitation and therefore contains no spatial information, the negative-sequence component contains spatial information in its phase. The Lorenz article teaches that the positive sequence component can be filtered off leaving only the negative-sequence component which can be fed to an observer used to extract flux angle position information.
Unfortunately, algorithms like the algorithm described in the Lorenz article only works well if an induction machine is characterized by a single sinusoidally distributed spatial saliency. As known in the art, in reality, motor currents exhibit more than a single spatial saliency in part due to the fact that PWM inverters produce a plethora of harmonics. As a result, the phase current negative sequence comprises a complicated spectrum that renders the method described in the Lorenz article relatively inaccurate.
Injection type saliency tracking algorithms employ a zero sequence high frequency current or voltage component instead of the negative sequence current component. One such technique is described in an article that issued in the IEEE IAS publication, pp. 2290-2297, Oct. 3-7, 1999, Phoenix Ariz., which is entitled xe2x80x9cA New Zero Frequency Flux Position Detection Approach For Direct Field Orientation Control Drivesxe2x80x9d (hereinafter xe2x80x9cthe Consoliarticlexe2x80x9d). The Consoli article teaches that the main field of an induction machine saturates during system operation which causes the spatial distribution of the air gap flux to assume a flattened sinusoidal waveform including all odd harmonics and dominated by the third harmonic of the fundamental. The third harmonic flux component linking the stator windings induces a third harmonic voltage component (i.e., a voltage zero sequence) that is always orthogonal to the flux component and that can therefore be used to determine the flux position. Unfortunately, the third harmonic frequency is low band width and therefore not particularly suitable for instantaneous position determination needed for low speed control.
The Consoli article further teaches that where a high frequency signal is injected into a rotating system, the injected signal produces a variation in the saturation level that depends on the relative positions of the main rotating field and high frequency rotating field. Due to the fundamental component of the main field, the impedance presented to the high frequency injected signal varies in space and this spatial variance results in an unbalanced impedance system. The unbalanced system produces, in addition to the fundamental zero sequence component of air gap flux and voltage, additional high frequency components having angular frequencies represented by the following equation:
xcfx89h1zs=xcfx89hxc2x1xcfx891xe2x80x83xe2x80x83Eq. 1 
where:
xcfx89h1zs=the high frequency voltage zero sequence component frequency;
xcfx89h=the high frequency injection signal frequency;
xcfx891=fundamental stator frequency first harmonic frequency; and
where the sign xe2x80x9cxc2x1xe2x80x9d is negative if the high frequency xe2x80x9cinjectedxe2x80x9d signal has a direction that is the same as the fundamental field direction and is positive if the injected signal has a direction opposite the fundamental field direction.
In this case, referring to FIGS. 2a and 2b, a zero sequence air gap flux component xcexhtzs that results from the complex interaction of the zero sequence flux produced by the fundamental component and the impressed high frequency injected signals induces a zero sequence voltage component Vhfzs on the stator winding that always leads the zero sequence flux component xcexhfzs by 90xc2x0. The maximum zero sequence flux component xcexhfzs always occurs when the main and high frequency rotating fields are aligned and in phase and the minimum zero sequence flux component xcexhfzs always occurs when the main and high frequency rotating fields are aligned but in opposite phase. Thus, in theory, by tracking the zero crossing points of the high frequency zero sequence component Vhfzs and the instances when minimum and maximum values of the high frequency zero sequence voltage component Vhfzs occur, the position of the high frequency rotating field xcex8h can be used to determine the main air gap flux position xcex8m.
For instance, referring to in FIGS. 2a and 2b, and also to FIGS. 9 and 10, at time t1 (see FIG. 9) when voltage Vhfzs is transitioning from positive to negative and crosses zero, the main field Fm is in phase and aligned with the high frequency flux xcexhfzs (i.e., field Fh) which lags voltage Vhfzs by 90xc2x0 and therefore main field angle xcex8m is xcex8hxe2x88x92xcfx80/2 (where xcex8h is the high frequency injected signal angle). As indicated in FIG. 2b, at time t1 voltage Vhfzs has a zero value. Nevertheless, in FIG. 9 voltage Vhfzs is illustrated as having a magnitude so that angle xcex8h is illustrated as having a magnitude so that angle xcex8h can be illustrated. Similar comments are applicable to FIG. 10 and time t3.
At time t2 where voltage Vhfzs reaches a minimum value, the main field Fm and flux xcexhfzs are in quadrature and therefore main field angle Fm can be expressed as xcex8hxe2x88x92xcfx80 (i.e., 90xc2x0 between signal Vhfzs and flux xcexhfzs and another 90xc2x0 between flux xcexhfzs and main field fm for a total of xcfx80). At time t3 (see FIG. 10) where voltage Vhfzs is transitioning from negative to positive through zero, the main field is out of phase with flux xcexhfzs and therefore main field angle xcex8m can be expressed as xcex8hxe2x88x923xcfx80/2. Similarly, at time t4 voltage Vhfzs reaches a maximum value with the main field Fm and flux xcexhfzs (i.e., field Fh) again in quadrature and main field Fm leading flux xcexhfzs and therefore main field angle xcex8m is equal to high frequency angel xcex8h.
Unfortunately, as in the case of the negative current component signal employed by Lorenz, high frequency zero sequence feedback signals contain a complicated harmonic spectrum mostly due to the PWM technique employed where the spectrum can be represented by the following equations:
xcfx89h1zs=xc2x1xcfx89hxc2x1xcfx891xe2x80x83xe2x80x83Eq. 2 
xcfx89h2zs=xc2x1xcfx89hxc2x1xcfx892xe2x80x83xe2x80x83Eq. 3 
xcfx89h4zs=xc2x1xcfx89hxc2x1xcfx894xe2x80x83xe2x80x83Eq. 4 
xcfx89h6zs=xcfx89hxc2x1xcfx896, etc.xe2x80x83xe2x80x83Eq. 5
where:
xcfx89h1zs, xcfx89h2zs, xcfx89h4zs, etc., are components of a harmonic spectrum of a high frequency current (or voltage) zero sequence signal and xcfx891, xcfx892, xcfx894, etc., are the 1st, 2nd, 4th, etc harmonic frequencies of the fundamental stator frequency. The xc2x1 signs are determined according to the convention described above with respect to Equation 1. The complicated zero sequence spectrum renders the method described in Consoli relatively inaccurate.
U.S. patent application Ser. No. 10/092,046 (hereinafter xe2x80x9cthe ""046 referencexe2x80x9d) which is entitled xe2x80x9cFlux Position Identifier Using High Frequency Injection With The Presence Of A Rich Harmonic Spectrum In A Responding Signalxe2x80x9d which was filed Mar. 5, 2002 and which is commonly owned with the present invention is incorporated herein by reference. Consistent with the comments above, the ""046 reference teaches that when a high frequency injection signal is injected into an induction based system which is operating at a stator fundamental frequency, the high frequency signal interacts with the stator field to generate a resulting high frequency current (and corresponding voltage) that has a complicated initial high frequency spectrum that includes a component at the injection frequency as well as components (hereinafter xe2x80x9csideband componentsxe2x80x9d) at various frequencies within sidebands about the injection frequency that are caused by inverter harmonics as well as interaction between system saliencies and the injected signals. The sideband components are at frequencies equal to the injection frequency plus or minus multiples of the fundamental frequency. For instance, where the injection frequency is 500 Hz and the fundamental frequency is 2 Hz, the sideband components may include frequencies of 494 Hz, 496 Hz, 498 Hz, 502 Hz, 504 Hz, 506 Hz, etc.
In addition, the ""046 reference recognizes that, given a specific motor control system configuration (i.e., specific hardware and programmed operation), a dominant sideband frequency has the largest amplitude. This dominant sideband frequency for the system configuration always corresponds to the sum of the injection frequency and a specific harmonic of the fundamental where the specific harmonic number is a function of system design and operating parameters. For instance, given a first system configuration, the system specific dominant sideband frequency may be the sum of the injection frequency and the 4th harmonic of the fundamental while, given a second system configuration, the system specific dominant sideband frequency may be the sum of the injection frequency and the 2nd harmonic of the fundamental frequency. The harmonic with the largest amplitude that is added to the injection frequency to obtain the dynamic sideband frequency corresponding to a specific system is referred to hereinafter as the system specific dominant harmonic number (DH). For instance, in the two examples above the system specific DHs are 4 and 2, respectively.
Moreover, the ""046 reference recognizes that during a commissioning procedure, the system specific DH can be determined using a FFT analysis or using a spectrum analyzer or some other similar type of device. Thus, in the case of the first and second exemplary systems above, the 4th and 2nd harmonics would be identified, respectively, as corresponding system specific DHs.
In light of the above realizations, the ""046 reference teaches a system designed to strip the injection frequency value out of each initial spectrum frequency thereby generating a low frequency spectrum including a separate frequency corresponding to each of the initial spectrum frequencies. For instance, in the above example where the fundamental and injection frequencies are 2 Hz and 500 Hz, respectively, and assuming sideband frequencies within the initial spectrum at 494 Hz, 496 Hz, 498 Hz, 502 Hz, 504 Hz and 506 Hz, after stripping, the low frequency spectrum includes modified sideband frequencies at xe2x88x926 Hz, xe2x88x924 Hz, xe2x88x922 Hz, 2 Hz, 4 Hz and 6 Hz.
After the low frequency spectrum value has been generated, the ""046 reference teaches that the low frequency spectrum can be divided by the system specific dominant harmonic number DH thereby generating a modified frequency spectrum where the dominant frequency value is the fundamental frequency (i.e., fundamental frequency value has the largest amplitude).
More specifically, at least one embodiment disclosed in the ""046 reference filters out the positive sequence components of the high frequency feedback currents and generates stationary high frequency a and 5-axis negative-sequence components. These stationary components are orthogonal and together include the noisy initial spectrum about the high injection frequency.
As well known in the art, in the case of any stationary to synchronous component signal conversion an angle that corresponds to the rotating components must be known. Where the angle is accurate, the resulting synchronous d and q-axis components are essentially DC values. However, where the angle is inaccurate, the resulting components fluctuate and the resulting d and q-axis components are not completely synchronous.
The ""046 reference teaches that a phase locked loop (PLL) adaptively generates a high frequency angle estimate that includes components corresponding to all high frequencies in the stationary xcex1 and xcex2-axis negative sequence components. The angle estimate is used to convert the stationary high frequency a and p-axis negative-sequence components to synchronous d and q-axis negative-sequence components. Thereafter, one of the d or q-axis components is negated and the resulting negated or difference value is fed to a PI controller or the like to step up the difference value and generate the low frequency spectrum.
The angle estimate is adaptively generated by adding the high injection frequency and the low frequency spectrum to generate a combined frequency spectrum and then integrating the combined frequency spectrum. Thus, the angle estimate is accurate when the combined frequency spectrum matches the actual frequency spectrum that exists in the stationary a and O-axis negative sequence components and, where there is a difference between the combined frequency spectrum and the stationary a and D-axis components, that difference is reflected in the synchronous d and q-axis components which adaptively drive the PI regulator and adjusts the low frequency spectrum.
The low frequency spectrum is combined mathematically with the system specific dominant harmonic number to generate a stator fundamental frequency estimate. After the stator frequency is identified, the stator frequency can be integrated to generate an air gap flux angle estimate Fm and other operating parameters of interest in control systems.
According to another embodiment described in the ""046 reference, instead of employing the three phase feedback currents to identify the complex frequency spectrum, a zero sequence voltage or current signal is employed. To this end, unlike the case where the high frequency current is resolved into quadrature d and q-axis components, the zero sequence embodiment includes a feedback loop that only senses and feeds back a single common mode component. With the zero sequence voltage (or current) feedback signal being a stationary xcex1-axis signal, an artificial stationary xcex2-axis signal is generated by integrating the xcex1-axis signal to generate an integrated signal, low pass filtering the integrated signal to generate a filtered signal and subtracting the filtered signal from the integrated signal thereby providing the high frequency component of the integrated signal as the xcex2-axis signal.
Consistent with the high frequency current example described above, after the xcex1 and artificial xcex2-axis components are generated, the stationary xcex1 and xcex2-axis signals are converted to synchronous high frequency d and q-axis signals and one of the d or q-axis signals is used to drive the PLL. Operation of the PLL in this embodiment is similar to operation of the embodiment described above.
While the concepts described in the ""046 reference are advantageous and suitable for certain applications where PLL capabilities are supported, in other cases such capabilities are not supported or preferably are not supported and therefore some other method for determining the main field flux angle in a rich harmonic system would be advantageous.
It has been recognized that the clearest and most accurately recognizable component of the high frequency zero sequence feedback signal and hence the component optimally used to identify the flux angle is the dominant harmonic component. It has also been recognized, however, that the dominant harmonic zero sequence feedback component cannot be employed directly in a Consoli type flux angle determining algorithm to yield accurate instantaneous flux angle values. To this end, assume that the fundamental frequency is 1 Hz, the frequency of the injected voltage is 500 Hz, a high frequency first harmonic is 501 Hz and that a high frequency second harmonic is 502 Hz. In addition, for the purposes of this explanation, assume that the high frequency second harmonic is the dominant harmonic component. Referring to FIGS. 3a and 3b, FIG. 3b includes waveforms Vh+1 and Vh+2 while FIG. 3a includes waveform xcex8h. Waveform Vh+1 is similar to waveform Vhfzs in FIG. 2b and corresponds to the 501 Hz high frequency first harmonic, waveform Vh+2 corresponds to the 502 Hz high frequency second harmonic. Wave form xcex8h is the instantaneous phase angle of the 500 Hz high frequency injected voltage.
According to Consoli, each instance corresponding to a zero crossing, maximum or minimum of the high frequency first harmonic Vh+1 can be used as a trigger to identify the main air gap flux angle xcex8m according to a standard set of four equations. Thus, for points 1 through 4 in FIG. 3a that correspond to a maximum value, a zero crossing from positive to negative, a minimum value and a zero crossing from negative to positive on the high frequency first harmonic Vh+1, respectively, the following equations can be used to identify angle xcex8m.
for points 1 and 5: "THgr"m="THgr"hxe2x88x922xcfx80xe2x80x83xe2x80x83Eq. 6
for points 2 and 6: "THgr"m="THgr"hxe2x88x92xcfx80/2xe2x80x83xe2x80x83Eq. 7 
for points 3 and 7: "THgr"m="THgr"hxe2x88x92xcfx80xe2x80x83xe2x80x83Eq. 8 
for points 4 and 8: "THgr"m="THgr"hxe2x88x923xcfx80/2xe2x80x83xe2x80x83Eq. 9 
respectively. Similarly, during the next cycle of the injected high frequency voltage, at points 5, 6, 7 and 8 corresponding to maximum, zero crossing from positive to negative, minimum and zero crossing from negative to positive instances of high frequency first harmonic Vh+1, equations 6-9 can be used, respectively, to identify angle xcex8m.
Points 1 and 5 define a main flux common equation line 200. As its label implies, line 200 corresponds to angles xcex8x that are phase shifted 2xcfx80 from the main flux angel xcex8m such that, if angle xcex8x can be determined at any point on line 200, angle xcex8m can be determined by subtracting 27 from the determined angle xcex8xxe2x80x94hence equation 6 above. Similarly; each of lines 202, 204 and 206 defined by point pairs 2 and 6, 3 and 7, and 4 and 8 is a main flux common equation line corresponding to angles xcex8x that are phase shifted xcfx80/2, xcfx80 and 3xcfx80/2 from main flux angle xcex8m.
Referring still to FIGS. 3a and 3b, while phase angle waveform xcex8h intersects each common equation line 200, 202, 204 and 206 at one of the high frequency first harmonic zero crossing, maximum or minimum instances and hence the angle xcex8x (i.e., xcex8h) can be determined at each of points 1 through 4, unfortunately, the zero crossing, maximum and minimum times of second harmonic Vh+2 do not similarly align with points 1 through 4 (i.e., do not align with the intersection of known common equation lines and injected angle waveform xcex8h). For example, as illustrated, a vertical line 210 corresponding to the maximum value of second harmonic waveform Vh+2 during the first illustrated cycle occurs before the vertical line 212 corresponding to the maximum value of first harmonic waveform Vh+1 and therefore would intersect waveform xcex8h before point 1. In this case Equation 6 above would not be valid. Similarly, each of the vertical lines (not separately labeled) corresponding to the positive to negative zero crossing, minimum value and negative to positive zero crossing of second harmonic waveform Vh+2 during the first illustrated cycle occur before the vertical lines corresponding to the positive to negative zero crossing, minimum value and negative to positive zero crossing of first harmonic waveform Vh+1 and therefore none of Equations 7-9 could be used to accurately determine angle xcex8m at those instances. It should be appreciated that the degree of phase shift between similar points (e.g., positive to negative zero crossings) on the first and second harmonic waveforms Vh+1 and Vh+2, respectively, changes during consecutive high frequency cycles and therefore is difficult to track.
Thus, Consoli""s Equations 6-9 above do not work with the high frequency second harmonic. Although not illustrated, the Consoli Equations also do not work with other dominant harmonics including the 4th, the 8th, etc., as the zero crossing and maximum and minimum times associated with those harmonics likewise do not align with points 1 through 4 (i.e., with intersecting points of common equation lines and the angle xcex8h of the high frequency injected signal).
Referring yet again to FIG. 3a, in addition to waveform xcex8h, FIG. 3a also includes a modified angle waveform xcex8hD that is determined by integrating the ratio of the frequency of the injected high frequency signal and the dominant harmonic number DH. Here, consistent with the present example where the injected signal has a frequency of 500 Hz and the dominant harmonic number DH is 2, angle xcex8hD corresponds to a frequency of 250 Hz (i.e., 500/2).
FIG. 3b includes waveform (Vh+2)/2 which corresponds to the high frequency second harmonic divided by two (i.e., the frequency is divided by 2). Thus, in the present example, waveform (Vh+2)/2 has a frequency of 251 (i.e., 502/2). Hereinafter waveform (Vh+2)/2 will be referred to as the modified second harmonic.
Referring specifically to waveforms xcex8hD and (Vh+2)/2, it should be appreciated that the times of the maximum, zero crossing from positive to negative, minimum and zero crossing from negative to positive instances align with points b, d, k and n on waveform xcex8hD where points b, d, k and n reside on common equation lines 200, 202, 204 and 206, respectively. Thus, at times corresponding to points b, d, k, and n equations similar to equations 6-9 above can be used to determine the main flux angle xcex8m, the only difference being that the instantaneous modified angle xcex8hD is substituted for the instantaneous high frequency angle xcex8h. Importantly, the maximum positive to negative zero crossing, minimum and negative to positive zero crossing times of modified second harmonic (Vh+2)/2 occur at positive to negative and negative to positive zero crossing times during two consecutive cycles of second harmonic Vh+2 and therefore can be easily determined from the second harmonic zero sequence feedback signal.
While using equations 6-9 at times corresponding to maximum, positive to negative zero crossing, minimum and negative to positive zero crossing instances of modified second harmonic (Vh+2)/2 advantageously yields four (e.g., at points b, d, k and n) flux angle xcex8m values every modified second harmonic cycle, four values per modified second harmonic cycle is only half the values that Consoli provides over the same cycle period. It has also bee recognized that four additional xcex8m values at points a, c, e and m (see again FIG. 3a) can be determined by identifying the maximum and minimum times of two consecutive cycles of second harmonic Vh+2 where points a and e correspond to consecutive maximum times and points c and m correspond to consecutive minimum times and solving equations similar to equations 6-9. For points a, c, e and m, as for points b, d, k and n, instantaneous angle xcex8hD is substituted for angle xcex8h. In addition, the shift angles are modified as points a, c, e and m reside on common equation lines 220, 222, 224 and 226 where the shift angels are 7xcfx80/4, xcfx80/4, 3xcfx80/f and 5xcfx80/r, respectively. The resulting equations for points a, b, c, d, e, k, m and n are:
for points a: xcex8m=xcex8hDxe2x88x927xcfx80/4xe2x80x83xe2x80x83Eq. 10 
for points b: xcex8m=xcex8hDxe2x88x922xcfx80xe2x80x83xe2x80x83Eq. 11 
xe2x80x83for points c: xcex8m=xcex8hDxe2x88x92xcfx80/4xe2x80x83xe2x80x83Eq. 12
for points d: xcex8m=xcex8hDxe2x88x92xcfx80/2xe2x80x83xe2x80x83Eq. 13 
for points e: xcex8m=xcex8hDxe2x88x923xcfx80/4xe2x80x83xe2x80x83Eq. 14 
for points k: xcex8m=xcex8hDxe2x88x92xcfx80xe2x80x83xe2x80x83Eq. 15 
for points m: xcex8m=xcex8hDxe2x88x925xcfx80/4xe2x80x83xe2x80x83Eq. 16 
for points n: xcex8m=xcex8hDxe2x88x923xcfx80/2xe2x80x83xe2x80x83Eq. 17 
Thus, for the first four points a, b, c and d the maximum, minimum and zero crossing times of a leading or first period of the second harmonic zero sequence feedback signal are used to determine main field flux angle xcex8m and, for the next four points e, k, m and n, the maximum, minimum and zero crossing times of a following or second period of the second harmonic zero sequence feedback signal are used to determine flux angle xcex8m so that angle xcex8mm is pieced together over consecutive high frequency cycles and performance as good as Consoli""s is achieved despite rich harmonics and a dominant harmonic number of two.
In the case of a system that generates a dominant fourth harmonic feedback signal (i.e., DH=4), angle "THgr"hD and hence "THgr"m are determined during four consecutive cycles of the fourth harmonic zero sequence signal. In this case, angle "THgr"hD is determined by integrating the ratio of the frequency of the injected voltage divided by dominant harmonic number DH=4 and sixteen equations similar to equations 10 through 17 are used to shift the resulting modified angle xcex8hD by different shift angles thereby generating sixteen angel xcex8m determinations (i.e., the same number of xcex8m determinations as provided by Consoli during the same period). As a general rule, the shift angles (i.e., the angles added to the dominant harmonic angles "THgr"hD) are multiples of 2xcfx80/4DH and thus the sixteen equations have different shift angles ranging from xcfx80/8 to 2xcfx80 separated by xcex/8.
Thus, one object of the invention is to provide a method and apparatus that identifies the main flux angle in rich harmonic systems that has performance characteristics similar to the characteristics of Consoli. As described above, the present invention performs as well as Consoli despite rich harmonics and irrespective of which harmonic is dominant in a feedback signal.
Another object is to provide a method and apparatus that accurately provides flux angle values in a rich harmonic system. Here instead of providing angle xcex8m estimates at the same rate as Consoli, in some embodiments where less frequent updates are required, fewer equations may be employed: For instance, instead of employing all eight Equations 10-17, one embodiment may employ only Equation 11, 13, 15 and 17 at corresponding times to identify xcex8m at points b, d, k and n.
Consistent with the above, the invention includes a method for use with a controller that uses a flux angle position value to control a three phase induction machine, the method for determining an instantaneous flux angle position value in the machine where the machine is characterized by a system specific dominant harmonic frequency number DH that is at least two, the method comprising the steps of injecting a high frequency voltage signal having a high frequency value into the machine thereby generating a high frequency current within the stator windings, obtaining a high frequency feedback signal from the machine, mathematically combining the high frequency value and the dominant harmonic number DH to provide an instantaneous modified angle, using the feedback signal to identify X consecutive calculating instances during each Y consecutive feedback signal cycles where Y is at least two, at each of the X different calculating instances, identifying an instantaneous flux angle position value by mathematically combining a shift angle with the modified angle where the shift angles corresponding to each of the X different calculating instances are all different and providing the instantaneous flux angle position value to the controller. Here the high frequency zero sequence signal may be either a high frequency zero sequence current feedback signal or a high frequency zero sequence voltage feedback signal.
The invention also includes a method for use with a controller that uses a flux angle position value to control a three phase induction machine, the method for determining an instantaneous flux angle position value in the machine where the machine is characterized by a system specific dominant harmonic frequency number DH that is at least two, the method comprising the steps of injecting a high frequency voltage signal having a high frequency value into the machine thereby generating a high frequency current within the stator windings, obtaining one of a high frequency zero sequence voltage feedback signal and a high frequency zero sequence current feedback signal from the machine, dividing the high frequency value and the dominant harmonic number DH to provide an instantaneous modified angle, using the feedback signal to identify four consecutive calculating instances during each of Y consecutive feedback signal cycles where Y is at least two, at each of the calculating instances during the Y consecutive feedback signal cycles, identifying an instantaneous flux angle position value by mathematically combining a shift angle with the instantaneous modified angle where the shift angles corresponding to each of the calculating instances during the Y consecutive feedback signal cycles are all unique shift angles and providing the instantaneous flux angle position value to the controller.
In addition, the invention includes a method for use with a controller that uses a flux angle position value to control a three phase induction machine, the method for determining an instantaneous flux angle position value in the machine where the machine is characterized by a system specific dominant harmonic frequency number DH that is at least two, the method comprising the steps of injecting a high frequency voltage signal having a high frequency into the machine thereby generating a high frequency current within the stator windings, obtaining one of a high frequency zero sequence voltage feedback signal and a high frequency zero sequence current feedback signal from the machine, integrating the feedback signal to generate a quadrature signal, identifying the zero crossing times of each of the feedback signal and the quadrature signal, dividing the high frequency by the dominant harmonic number DH to provide an instantaneous modified angle, at each of the zero crossing times during DH consecutive feedback signal cycles, identifying an instantaneous flux angle position value by mathematically combining a shift angle with the instantaneous modified angle where the shift angles corresponding to each of the zero crossing times during the DH consecutive feedback signal cycles are all unique shift angles and are multiples of 2xcfx80/4DH and providing the instantaneous flux angle position value to the controller.
Furthermore, the invention includes an apparatus for use with a controller that uses a flux angle position value to control a three phase induction machine, the apparatus for determining an instantaneous flux angle position value in the machine where the machine is characterized by a system specific dominant harmonic frequency number DH that is at least two, the apparatus comprising a programmed processor performing the steps of: injecting a high frequency voltage signal having a high frequency value into the machine thereby generating a high frequency current within the stator windings, obtaining a high frequency feedback signal from the machine, mathematically combining the high frequency value and the dominant harmonic number DH to provide an instantaneous modified angle, using the feedback signal to identify X consecutive calculating instances during each Y consecutive feedback signal cycles where Y is at least two, at each of the X different calculating instances, identifying an instantaneous flux angle position value by mathematically combining a shift angle with the instantaneous modified angle where the shift angles corresponding to each of the X different calculating instances are all different and providing the instantaneous flux angle position value to the controller.
These and other objects, advantages and aspects of the invention will become apparent from the following description. In the description, reference is made to the accompanying drawings which form a part hereof, and in which there is shown a preferred embodiment of the invention. Such embodiment does not necessarily represent the full scope of the invention and reference is made therefore, to the claims herein for interpreting the scope of the invention.